Excellent question!
The coldness that you feel when you are outside on
a winter day is from your body and the outside air
trying to become the same temperature. You lose
body heat trying to warm up the environment--
since there's much more of it than there is of
you. Heat "travels" in a few different ways:
conduction, convection, and radiation. For
a fabric or jacket to be insulating, you want to
slow down the transfer of your body heat to the
environment.

The first method is to have a fabric that is
very thick or has a lot of loft. A good example is
fleece. Fleece is a fabric that is knit and then
brushed so that it almost looks like fur. The fur
"pile" traps still air, and the thicker the
fleece, the more difficult it is for heat to
escape. Thicker does not necessarily mean heavier
though, you can have a thick fabric that weighs
the same as a thin fabric. This is why fleeces
became so popular because their loft is usually
very good for their weight. We are slowing down
conduction in this case because it's hard for heat
to move through a thicker barrier.

However, most fleeces let wind come right through.
Moving air feels cold because it moves heat away
via convection. For this, we can use a fabric with
low air permeability to feel warmer. An example of
this is a "windbreaker" or any rain jacket.
These fabrics let less wind come through because
they are woven tightly (have less spaces/holes in
the fabric) or have a waterproof coating (think of
it like a plastic bag "film" attached to the
fabric). The downside is that if you are sweating
a lot, these types of jackets can feel clammy
because your sweat can't evaporate through the
fabric to keep you comfortable-- this steam-room
effect can actually chill you in the same way a
light breeze cools you off more when you're
sweating and exercising than when you're already
dry and comfortable.

The last way we can insulate is preventing heat
loss via radiation. Emergency blankets are
metallic looking because they reflect infrared
radiation coming from your body back to you.
Infrared radiation is the same thing that makes
sunlight on your skin feel warm, although the sun
emits a lot more infrared radiation than a human
body. Why aren't there metallic-fabric jackets?
Well, we're starting to see some, but most
metallic-looking fabrics are loud, crunchy, and
uncomfortable since they "breathe" worse than
windbreaker/rain jacket-type fabric. The tradeoff
isn't worth it for most people and climates.

So to summarize, different types of fabrics
insulate better because they slow down your body
heat from escaping via
conduction/convection/radiation. Some are thicker,
some are more windproof because their structure
lets less air through, and some can be reflective
to bounce infrared radiation back to your body.

Usually, you need to use multiple fabrics to
accomplish this, so bundle up by layering!
My go-to system is either wearing a fleece
underneath a rain shell, or a down jacket where
you have tightly woven fabric sandwiching
incredibly lofty goose down/feathers. Just don't
over-do it to the point where you get too hot and
sweat =)

Andrew, Materials Coordinator, The North Face

(please note the opinions and facts shared
above are that of the individual and do not
represent those of The North Face)

Answer 2:

There is a property of a material called
"thermal effusivity," that basically
describes how easily the material loses heat to
the environment, and how much heat it holds in
general. So, it combines the ideas of heat
capacity (which is how much head a material
can hold) and thermal diffusivity (how
quickly it gives away the heat). Whether this
property is low or high depends on many factors.
There is the chemical part (what compounds and
molecules the materials is made of) but also a
physical structure and packing part (for example,
down feathers hold a lot of heat, due to their
structure, or, clothing with layers keeps in more
heat).

By looking at the chemical makeup of the
clothing and the physical structure of it, you can
determine how well it will insulate.

Answer 3:

Fabric insulates by trapping air between it and
within it. Air that isn't moving can still
transfer heat by conduction, but not by
convection, which is the most effective
method of moving heat.

Answer 4:

So the key concept which you probably already
understand is that when you have something hot
next to something colder, heat flows from the hot
object to the colder object. This process is
called heat transfer and is unavoidable,
but by using insulation, the rate of heat transfer
can be reduced. Heat transfer happens by molecules
colliding with each other which transfers some
energy. Some materials don’t transfer as much
energy when molecules collide into them. These
materials are called insulators and are important
in a lot of different places. For instance, there
is insulation in the walls of your house so that
when it’s a cold day, your house doesn’t get cold.
In general, the substances that transfer heat the
fastest are solids, followed by liquids, then
gases. An interesting application of insulators is
if you wear a jacket when it is cold out. The
jacket doesn’t actually provide any heat the way a
radiator does, but what it does do is that is
slows down the rate at which heat leaves your body
into the air.